Ex 11.4, 8 - Find equation: Vertices (0, 5), foci (0, 8) - Hyperbola

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  1. Chapter 11 Class 11 Conic Sections
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Ex 11.4, 8 Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ±5), foci (0, ±8) We need to find equation of hyperbola given Vertices (0, ±5), foci (0, ±8) Since Vertices are on the y-axis So required equation of hyperbola is ﷐𝑦2﷮𝑎2﷯ – ﷐𝑥2﷮𝑏2﷯ = 1 We know that Vertices =(0, ±a) Given Vertices = (0, ±5) So a = 5 a2 = 25 Foci are (0, ± c) Given foci are (0, ±8) So c = 8 Axis of hyperbola is y−axis c2 = a2 + b2 (8)2 = (5)2 + b2 b2 = 64 − 25 b2 = 39 Required equation of hyperbola is ﷐𝑦2﷮𝑎2﷯ − ﷐𝑥2﷮𝑏2﷯ = 1 Putting values ﷐𝒚𝟐﷮𝟐𝟓﷯ − ﷐𝒙𝟐﷮𝟑𝟗﷯ = 1

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